This rugged peak is located at the southern end of the Organ Mountains in southern New Mexico. It is a prominent landmark along I-10 between Las Cruces, NM and El Paso, TX. Bishop Cap is composed primarily of limestone and other sedimentary rocks and there are exposed cliff bands that nearly encircle the peak.
There are no established trails on this peak, but there is a newly developed mountain bike trail (Sierra Vista) that travels just to the west of the mountain. One of the closest points to access this trail begins by exiting I-10 at exit #151 south of Las Cruces. From the interstate exit head east towards Bishop Cap (it is easily discernable from the exit). The road turns to gravel after a short bit, and 2.1 miles you'll have to take a sharp left to avoid entering a sand and gravel operation. At 2.9 miles from the interstate you'll pass Dona Ana County liquid waste disposal and the road will get a little bit rougher. At about 4.6 miles there is a parking area on the north side of the road. I was able to drive my Toyota Camry to the parking area without any problems.
None, that I know about.
Follow BLM land camping policies.
The parking area also services the Pena Blanca (aka Volcano) bouldering area to the north. It is about a mile hike in along a washed out road to reach some very good Southern NM bouldering.
"God bless America. Let's save some of it."